# Michael's triangle

Geometry Level 4

In quadrilateral $$ABCD,$$ $$AB = AD = 1,$$ $$BD = \sqrt{2},$$ $$BC = \dfrac{ \sqrt{2} }{ 2 },$$ and $$CD = \dfrac{ \sqrt{6} }{ 2}.$$ The area of triangle $$ABC$$ can be expressed in the form $$\dfrac{\sqrt{a} + b}{c}$$, where $$a,$$ $$b,$$ and $$c$$ are positive integers and $$a$$ is square-free. What is the value of $$a+b+c$$?

This problem is posed by Michael T.

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